Pullback attractors for globally modified Navier-Stokes equations with infinite delays

We establish the existence of pullback attractors for thedynamical system associated to a globally modified model ofthe Navier-Stokes equations containing delay operators withinfinite delay in a suitable weighted space. Actually, weare able to prove the existence of attractors in different classes ofuniverses, one is the classical of fixed bounded sets, andthe other is given by a tempered condition. Relationshipbetween these two kind of objects is also analyzed.